Denote a kind of path-star forest by \(F(k_1, k_2; \ell )=k_1P_{2\ell }\cup k_2S_{2\ell -1}\) . Lidický et al. [1]} investigated the Turán number of \(F(k_1, k_2; 2)\)  for sufficiently large \(n\) . Lan et al. [2]} considered the Turán number of \(F(k_1, k_2; 2)\)  for \(n\geqslant 10k_1+13k_2+3\) . Later, Zhang and Wang [3]} considered the Turán number of \(F(k_1, k_2; 3)\)  for \(n\geqslant 23k_1+31k_2+3\)  and proposed Conjecture REF .
